scholarly journals Global solvability and asymptotic behavior for a nonlinear coupled system of viscoelastic waves with memory in a noncylindrical domain

2007 ◽  
Vol 325 (2) ◽  
pp. 1077-1094 ◽  
Author(s):  
M.L. Santos ◽  
M.P.C. Rocha ◽  
P.L.O. Braga
Keyword(s):  
Asymptotic Behavior ◽  
Coupled System ◽  
Global Solvability ◽  
Noncylindrical Domain ◽  
Viscoelastic Waves ◽  
Nonlinear Coupled System ◽  
With Memory

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

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